Raman scattering spectroscopy is widely used as an analytical technique in various fields, but its measurement process tends to be slow due to the low scattering cross-section. In the last decade, various broadband coherent Raman scattering spectroscopy techniques have been developed to address this limitation, achieving a measurement rate of 500 kSpectra/s. Here, we present a substantially increased measurement rate of 50 MSpectra/s, which is 100 times higher than the previous state-of-the-art, by developing time-stretch coherent Raman scattering spectroscopy. Our newly developed system, based on a mode-locked Yb fiber laser, enables highly efficient broadband excitation of molecular vibrations via impulsive stimulated Raman scattering with an ultrashort femtosecond pulse and sensitive time-stretch detection with a picosecond probe pulse at a high repetition rate of the laser. As a proof-of-concept demonstration, we measure broadband coherent Stokes Raman scattering spectra of organic compounds covering the molecular fingerprint region from 200 to 1,200 cm^-1. This high-speed broadband vibrational spectroscopy technique holds promise for unprecedented measurements of sub-microsecond dynamics of irreversible phenomena and extremely high-throughput measurements.